Answer :
The angle B in triangle ABC is approximately 88.23 degrees. We can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
The formula is as follows:
[tex]c^2 = a^2 + b^2 - 2ab * cos(B)[/tex]
Given that b = 98.5 cm, a = 123.7 cm, and c = 154.9 cm, we can substitute these values into the formula:
[tex]154.9^2 = 123.7^2 + 98.5^2 - 2 * 123.7 * 98.5 * cos(B)[/tex]
Expanding this equation, we get:
24003.01 = 15294.69 + 9702.25 - 24279.95 * cos(B)
Combining like terms, we have:
24003.01 = 24996.94 - 24279.95 * cos(B)
Rearranging the equation, we get:
-996.93 = -24279.95 * cos(B)
Now, we can solve for cos(B):
cos(B) = -996.93 / -24279.95
cos(B) = 0.0411
Using the inverse cosine function [tex](cos^-1)[/tex], we can find the angle B:
B = [tex]cos^-1(0.0411)[/tex]
B = 88.23 degrees (rounded to two decimal places)
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